The API call get_linked_pathways is a bit of a misnomer, because said API returns what is shown under "Related pathway" in the web interface.

For example, the related pathways of http://www.genome.jp/dbget-bin/www_bget?pathway+eco00620 coincide with the get_linked_pathways API call (in Ruby):

require 'soap/wsdlDriver'

# Pathway we want to investigate:
PATHWAY_ID = 'eco00620'

# Get web service description and create a local surrogate for the service:
wsdl = "http://soap.genome.jp/KEGG.wsdl"
serv = SOAP::WSDLDriverFactory.new(wsdl).create_rpc_driver
serv.generate_explicit_type = true

# Retrieve array of linked pathway IDs:
linked_pathways = serv.get_linked_pathways("path:#{PATHWAY_ID}")
linked_pathways.each { |pathway|
    puts "#{pathway}"
}

To answer your question: related pathways are "linked" together by manual curation.

I could not find an exact statement about the curation process on the KEGG web site, but can find some more information on it in this book: http://books.google.ca/books?id=ZEnMV6KvBzwC&pg=PA297&lpg=PA297&dq=kegg+pathway+curation

Some rather general statement on the curation process has also been made in M. Kanehisa et.al., "KEGG for linking genomes to life and the environment", Nucleic Acids Res. 2008 January; 36(Database issue): D480–D484. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2238879/

Hope this helps.